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1. Lecture 13.1

2. Chapter 34. Electromagnetic Induction This chapter: Changing magnetic field creates electric field (induced electric field) The Next chapter: Changing electric field creates magnetic field. Magnetism Move charges generate magnetic field Magnetic field exerts force on moving charges Electrics Electric charges generate electric field Electric field exerts force on electric charges

3. Chapter 34. Electromagnetic Induction Question: How do we transform the kinetic energy of the windmill into electric energy that we can use?

4. Two different ways to generate an EMF: • Using nonelectrostatic force (battery) • Moving a conductor in magnetic field (motional emf) The electric field in conductor is such that the electric force precisely balances the magnetic force, so that the total force acting on a charge in the conductor is zero.

5. Motional emf The motional emf of a conductor of length l moving with velocity v perpendicular to a magnetic field B is

6. Example: Sliding Wire

7. A square conductor moves through a uniform magnetic field. Which of the figures shows the correct charge distribution on the conductor?

8. A square conductor moves through a uniform magnetic field. Which of the figures shows the correct charge distribution on the conductor?

9. Is there an induced current in this circuit? If so, what is its direction? • No • Yes, clockwise • Yes, counterclockwise

10. Is there an induced current in this circuit? If so, what is its direction? • No • Yes, clockwise • Yes, counterclockwise

11. Magnetic flux can bedefined in terms of an area vector

12. Lenz’s Law There is an induced current in a closed, conducting loop if and only if the magnetic flux through the loop is changing. The direction of the induced current is such that the induced magnetic field opposes the change in the flux. Lenz’s law explains motional EMF.

13. Faraday’s Law An emf is induced in a conducting loop if the magnetic flux through the loop changes. The magnitude of the emf is and the direction of the emf is such as to drive an induced current in the direction given by Lenz’s law.

14. Magnetic data storage encodes information in a pattern of alternating magnetic fields. When these fields move past a small pick-up coil, the changing magnetic field creates an induced current in the coil. This current is amplified into a sequence of voltage pulses that represent the 0s and 1s of digital data.

15. A square loop of copper wire is pulled through a region of magnetic field. Rank in order, from strongest to weakest, the pulling forces Fa, Fb, Fc and Fd that must be applied to keep the loop moving at constant speed. • Fb = Fd > Fa = Fc • Fc > Fb = Fd > Fa • Fc > Fd > Fb > Fa • Fd > Fb > Fa = Fc • Fd > Fc > Fb > Fa

16. A square loop of copper wire is pulled through a region of magnetic field. Rank in order, from strongest to weakest, the pulling forces Fa, Fb, Fc and Fd that must be applied to keep the loop moving at constant speed. • Fb = Fd > Fa = Fc • Fc > Fb = Fd > Fa • Fc > Fd > Fb > Fa • Fd > Fb > Fa = Fc • Fd > Fc > Fb > Fa

17. A current-carrying wire is pulled away from a conducting loop in the direction shown. As the wire is moving, is there a cw current around the loop, a ccw current or no current? • There is no current around the loop. • There is a clockwise current around the loop. • There is a counterclockwise current around the loop.

18. A current-carrying wire is pulled away from a conducting loop in the direction shown. As the wire is moving, is there a cw current around the loop, a ccw current or no current? • There is no current around the loop. • There is a clockwise current around the loop. • There is a counterclockwise current around the loop.

19. Lecture 13.2 • Induced Currents and Induced Fields • Inductors, LC Circuits and LR Circuits

20. Review of Faraday’s Law and Lenz’s Law • Faraday: Change of magnetic flux induces EMF: • Lenz: The direction of induced EMF is such as to oppose the change of flux

21. A More Correct Version of Faraday’s Law Assign a positive direction (counterclockwise) to the loop under consideration Use right hand rule, give a positive direction to the magnetic field This defines the sign for the magnetic flux A positive induced EMF leads to counterclockwise current A negative induced EMF leads to clockwise current The – sign is required by Lenz’s law

22. Review: Sliding wire in B field • The induced current resists the change of flux • The magnetic force on the wire resists the change of flux, i.e. resists the motion. •  The magnetic force is antiparallel to v. • This is also required by energy conservation!

23. A conducting loop is halfway into a magnetic field. Suppose the magnetic field begins to increase rapidly in strength. What happens to the loop? • The loop is pulled to the left, into the magnetic field. • The loop is pushed to the right, out of the magnetic field. • The loop is pushed upward, toward the top of the page. • The loop is pushed downward, toward the bottom of the page. • The tension is the wires increases but the loop does not move.

24. A conducting loop is halfway into a magnetic field. Suppose the magnetic field begins to increase rapidly in strength. What happens to the loop? • The loop is pulled to the left, into the magnetic field. • The loop is pushed to the right, out of the magnetic field. • The loop is pushed upward, toward the top of the page. • The loop is pushed downward, toward the bottom of the page. • The tension is the wires increases but the loop does not move.

25. Generator: transforming mechanical energy to electric energy

26. Metal Detector

27. Inductor and Self-Inductance

28. Inductance of a solenoid The inductance of a solenoid having N turns, length l and cross-section area A is

29. The potential difference across an inductor Faraday’s law: Change of flux leads to induced emf that opposes the flux change. The potential difference across an inductor with an inductance of L and carrying a current I is

30. Energy in Inductors and Magnetic Field • It is really magnetic field energy that is stored inside an inductor!

31. The current in an LC circuit The current in an LC circuit where the initial charge on the capacitor is Q0 is The oscillation frequency is given by

32. The potential at a is higher than the potential at b. Which of the following statements about the inductor current I could be true? • I is from b to a and is steady. • I is from b to a and is increasing. • I is from a to b and is steady. • I is from a to b and is increasing. • I is from a to b and is decreasing.

33. The potential at a is higher than the potential at b. Which of the following statements about the inductor current I could be true? • I is from b to a and is steady. • I is from b to a and is increasing. • I is from a to b and is steady. • I is from a to b and is increasing. • I is from a to b and is decreasing.

34. LR circuits

35. LR circuits

36. Rank in order, from largest to smallest, the time constants τa, τb, and τc of these three circuits. • τa > τb > τc • τb > τa > τc • τb > τc > τa • τc > τa > τb • τc > τb > τa

37. Rank in order, from largest to smallest, the time constants τa, τb, and τc of these three circuits. • τa > τb > τc • τb > τa > τc • τb > τc > τa • τc > τa > τb • τc > τb > τa

38. EXAMPLE 34.15 An AM radio oscillator QUESTION:

39. EXAMPLE 34.15 An AM radio oscillator

40. Chapter 34. Summary Slides

41. General Principles